List questions from compactness

Published on 24 Mar 2026 - 22:08

962

Views

$X$ a compact Hausdorff space and a sequence $A_1 \supset A_2 \supset \dots$ of closed connected subsets. Show that $\bigcap A_n$ is also connected.

Published on 25 Mar 2026 - 23:11

123

Views

$\prod X_{a\in A} $ with the box topology is compact, show that $X_a$ is compact for every $a\in A$

Published on 11 May 2018 - 13:16

6.9k

Views

Show that unit circle is not homeomorphic to the real line

Published on 12 May 2018 - 16:38

50

Views

Compact by Sequences

Published on 12 May 2018 - 18:17

233

Views

Defined integral over a closed and bounded subset of $\mathbb{R}$

Published on 12 May 2018 - 19:15

55

Views

Make non-compact subspaces compact

Published on 12 May 2018 - 20:40

38

Views

1) Prove that T(K) = [-A,A] where A = $\sqrt{\sum_{i=1}^p (a_i)^2}$

Published on 12 May 2018 - 21:29

43

Views

Find the extrema of a linear form on a unit ball

Published on 13 May 2018 - 1:50

38

Views

How can we justify that we can generate random point on a compact set with all point being equally likely ?

Published on 25 Mar 2026 - 17:39

115

Views

Prove that f(x) vanishes in whole of its domain.

Published on 26 Mar 2026 - 4:53

453

Views

Compact sets of Moore plane

Published on 13 May 2018 - 14:37

810

Views

Compact metric spaces can be covered by finitely many $\epsilon$-balls

Published on 13 May 2018 - 16:06

40

Views

Show that the mapping $x^\mapsto x^(x)+r$ is weak$^*$ continuous

Published on 26 Mar 2026 - 6:34

1.1k

Views

Total derivative vanishes implies function is constant

Published on 15 May 2018 - 18:02

List Question

Is there such subsequence in $L^2(\Bbb{R}^2)$.

$X$ a compact Hausdorff space and a sequence $A_1 \supset A_2 \supset \dots$ of closed connected subsets. Show that $\bigcap A_n$ is also connected.

$\prod X_{a\in A} $ with the box topology is compact, show that $X_a$ is compact for every $a\in A$

Show that unit circle is not homeomorphic to the real line

Compact by Sequences

Defined integral over a closed and bounded subset of $\mathbb{R}$

Make non-compact subspaces compact

1) Prove that T(K) = [-A,A] where A = $\sqrt{\sum_{i=1}^p (a_i)^2}$

Find the extrema of a linear form on a unit ball

How can we justify that we can generate random point on a compact set with all point being equally likely ?

Prove that f(x) vanishes in whole of its domain.

Compact sets of Moore plane

Compact metric spaces can be covered by finitely many $\epsilon$-balls

Show that the mapping $x^\mapsto x^(x)+r$ is weak$^*$ continuous

Total derivative vanishes implies function is constant

Trending Questions

Popular # Hahtags

Popular Questions